I have a regression model with regression coefficients $\beta_j$, $j=1,...,n$, and I would like to use a LASSO prior for $\beta_j$, this is:

$$\beta_j \sim Laplace(0,1/\lambda),$$

where the Laplace density function is $\pi(\beta_j\vert b) = \dfrac{1}{2b}\exp\left(-\dfrac{\vert \beta_j \vert}{b}\right)$. What priors are typically used in the literature for $\lambda$? I was thinking of using a "non informative" Gamma or Inverse Gamma, but I wanted to check if there are some better choices?